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# Quick Help on Algebra

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Adam and Barb had a book sale over the weekend. Adam sold 4 hardcover books and ten paperbacks. Barb sold 5 hardcover books and 7 paperbacks for the same prices each. Adam sold \$62 worth of books while Barb sold \$61 worth. How much did they charge for hardcovers and how much for paperbacks?

What is the innequality equation

Guest Sep 23, 2017
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#1
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The word problem is asking you to create an inequality that accuratly represents the amount that they charge for hardcovers compared to paperbacks.

Guest Sep 23, 2017
#2
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We don't have an "inequality" here....just a system of equations

Let P be the price of a paperback and H be the price of a hardcover book

And  we have that

10P  + 4H  =  62       ⇒  this represents Adam's situation   (1)

7P   + 5H  =  61      ⇒   this reperesents Barb's siutation   (2)

Multiply  (1) through by  5  and (2) through by -4   and add them together

So we have

50P  + 20H  =  310

-28P - 20h  =   -244

________________

22P      =            66                     divide by  22 on both sides

P  = 3     this is the price of a paperback  [in dollars]

And using (1) to find H, we have

10 (3)  + 4H   = 62

30  + 4H  = 62         subtract 30 from both sides

4H  = 32                   divide by 4 on both sides

H  = 8    this is the price of a hradcover book [ in dollars]

CPhill  Sep 23, 2017

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